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Energy-Preserving Time-Varying Schroeder Allpass Filters and Multichannel Extensions

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We propose time-varying Schroeder allpass filters and Gerzon allpass reverberators that remain energy preserving irrespective of arbitrary variation of their allpass gains or feedback matrices over time. We propose various ways of realizing the unitary matrix involved in the Schroeder structure, based on classic ladder and lattice filters and their generalizations. We show how to construct more elaborate structures including nestings and cascade, giving various strategies for reducing their implementation cost. Extending these algorithms to the multi-input, multi-output case yields time-varying, energy-preserving generalizations of Gerzon’s reverberator, providing a link between Schroeder allpass filters and Schelcht’s recently proposed “Allpass Feedback Delay Networks.” Stability proofs are given for common uses of Schroeder allpass filters, such as inside of Feedback Delay Network reference structures. Finally we give a substantial review of the properties of time-invariant Schroeder allpass filters.

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JAES Volume 69 Issue 7/8 pp. 465-485; July 2021
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